US President Donald Trump on Saturday sent "warm greetings" to Muslims celebrating the end of Ramadan, after his administration broke with the tradition of hosting a White House event to recognize the holy month.

"On behalf of the American people, Melania and I send our warm greetings to Muslims as they celebrate Eid al-Fitr," Trump said in a statement. "During this holiday, we are reminded of the importance of mercy, compassion, and goodwill."

"With Muslims around the world, the United States renews our commitment to honor these values."

Since the Bill Clinton administration, the White House has each year hosted either an event to mark the Eid al-Fitr feast -- which ends the fasting month of Ramadan -- or a meal breaking the dawn-til-dusk fast, known as an iftar.

Secretary of State Rex Tillerson reportedly rejected a request by his department's office of religion and global affairs to hold an event for the holiday.

Trump has come under fire for his history of anti-Muslim rhetoric on the campaign trail, that included calls for surveillance of US mosques and an outright ban on Muslims entering the country in the name of national security.

A week after becoming president he issued a ban on travelers from several predominantly Muslim countries, which has been frozen by the US courts after sparking global chaos and outrage.

Yet during a visit to Saudi Arabia last month, Trump softened his tone on Islam, rejecting the idea of a battle between religions in an address before dozens of leaders of Muslim countries.